Yes there are 4 mounts all together, 2 that connect the drive train to the body in the wheel wells and 2 that connect it to the sub-frame front and rear. The 2 mounts in the wheel wells will require you to lower the sub-frame with the engine and trans to replace. The rear mount will require you to suspend the engine in the car and lower the back of the sub-frame to replace. Unless the rear mount has been oil saturated it almost never goes bad because the natural torque of the engine pushes down on the rear mount. The sway your feeling might be loose sub-frame bolts, I would check and make sure they are tight before replacing the motor mounts.
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There is no replacement for displacement!